The Lelek fan and the Poulsen simplex as Fraïssé limits

摘要: We describe the Lelek fan, a smooth fan whose set of end-points is dense, and Poulsen simplex, Choquet simplex extreme points as Fraisse limits in certain natural categories embeddings projections. As an application we give short proof their uniqueness, universality, almost homogeneity. further show that for every two countable dense subsets there exists auto-homeomorphism mapping one onto other. This improves result Kawamura, Oversteegen, Tymchatyn from 1996.